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1

Negotiable Auction based on Mixed Graph: ANovel Spectrum Sharing Framework

Huiyang Wang, Diep N. Nguyen, Eryk Dutkiewicz, Gengfa Fang, and Markus Dominik Mueck

Abstract—Auction-based spectrum sharing is a promisingsolution to improve the spectrum utilization in 5G networks.Along with the spatial reuse, we observe that the ability toadjust the coverage of a spectrum bidder can provide room toitself for further negotiation while auctioning. In this work, wepropose a novel economic tool, Size-Negotiable Auction Mecha-nism (SNAM), which provides a hybrid solution between auctionand negotiation for multi-buyers sharing spectrum chunks froma common database. Unlike existing auction-based spectrumsharing models, each bidder of the SNAM submits its bid forusing the spectrum per unit space and a set of coverage rangesover which the bidder is willing to pay for the spectrum. Theauctioneer then coordinates the interference areas (or coveragenegotiation) to ensure no two winners interfere with each otherwhile aiming to maximize the auction’s total coverage areaor revenue. In this scenario, the undirected graph used byexisting auction mechanisms fails to model the interferenceamong bidders. Instead, we construct a mixed interferencegraph and prove that SNAM’s auctioning on the mixed graphis truthful and individually rational. Simulation results showthat, compared with existing auction approaches, the proposedSNAM dramatically improves the spatial efficiency, hence leadsto significantly higher seller revenue and buyer satisfaction undervarious setups. Thanks to its low complexity and low overhead,SNAM can target fine timescale trading (in minutes or hours)with a large number of bidders and requested coverages.

Index Terms—Spectrum auction, licensed shared access, truth-fulness, joint auction and negotiation, multi-attribute auction.

I. INTRODUCTION

RECENT years have witnessed a growing interest fromboth academia and industry in spectrum sharing for

5G networks. Trading spectrum online is considered as apromising solution to improve the spectrum utilization. Thelargest telecommunications standard bodies like the FederalCommunications Commission (FCC) and the European T-elecommunications Standardization Institute (ETSI) have beendeveloping future spectrum management architectures thatconsider spectrum sharing as a core feature. These architec-tures are referred to as Spectrum Access Systems (SAS) byFCC and Licensed Shared Access (LSA) by ETSI [2] [3].

Manuscript received September 15, 2016; revised April 20, 2017 and June27, 2017; accepted July 8, 2017. This work has been supported in part by In-tel’s University Research Office and Australian Research Council (DiscoveryEarly Career Researcher Award DE150101092). Preliminary results in thisarticle were presented at the IEEE DySPAN 2015 Conference [1].

H. Wang, D. N. Nguyen, E. Dutkiewicz and G. Fang are with theSchool of Electrical and Data Engineering, University of TechnologySydney, NSW 2007, Australia (e-mail: huiyang.wang@student.uts.edu.adu;diep.nguyen@uts.edu.au; eryk.dutkiewicz@uts.edu.au; gengfa.fang@uts.edu.au).

M. Mueck is with Intel Mobile Communications, 85779 Munich, Germany(e-mail: markus.dominik.mueck@intel.com).

Operator AOperator C

Incumbent

Operator B

Operator A

LSA

Controller

Incumbent 1LSA

RepositoryIncumbent 2

Incumbent 3

...

Mobile devices can not

only use primary band,

but also the LSA band.

LSA Licensed Base station

controls mobile devices to

access the LSA band

Allocate LSA

bands to Base

stations and

withdraw them

as wellReport available

spectrum for trading

LSA Bands

Primary Bands

Fig. 1. LSA architecture. Incumbents will provide the available spectrum tothe LSA system, while the secondary base stations will be informed by theLSA system and then bid for the spectrum.

Both SAS and LSA support to open licensed but underutilizedspectrum bands of primary/Incumbent users for secondary use.

Among network economic models, auction-based spectrumtrading has been widely used with a long lasting history.Numerous auction-based spectrum sharing models have beenproposed. However, compared with negotiation, auction stiflescommunications between the bidders and the sellers [4]. More-over, along with the spatial reuse, we observe that the abilityto adjust the coverage of a spectrum bidder is also a uniquefeature of radio spectrum, compared with general merchandiseitems in conventional auctions. This distinguished characterlends bidders room for further negotiation while auctioning.This work explores a hybrid approach between auction andnegotiation for spectrum sharing.

Unlike traditional spectrum sales that often involve a longcontracts (e.g. multi-year) and large coverage areas (e.g.,country, cities), spectrum sharing in future networks likelyinvolves much shorter contracts over much smaller cover-age areas. The number of bidders under the new spectrumtrading is likely larger than that under the traditional oneand with much more heterogeneous coverage requirements.For secondary licensees, their requirements are based ondifferent deployments and transmission distances. Moreover,with the trend of cellular densification (micro-, femto-cells),an increasing number of base stations also makes the spectrummarket more competitive and complicated.

To accommodate the above heterogeneity, spectrum bid-ders need to simultaneously negotiate/auction on variousfeatures/attributes. Note that existing auction-based spectrumsharing schemes (e.g., [5] [6] [7] [8] [9] [10]) often only

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considered bidders’ payment. In such cases, single-attributeauctions were often recruited and proved to be an efficient tool(with regards to both economic- and operation- robustness). Inthis work, to account for coverage negotiation (in addition tothe payment), we design a multi-attribute auction mechanism[11] so that both payments and coverage ranges for auctionwinners can be determined.

To facilitate the interference coordination/negotiation at theauctioneer, a graph whose vertices represent bidders andedges represent interference between them (i.e., those can’tco-exist) is often used (e.g., [6] [7] [8] [9] [10]). In sucha graph, vertices/bidders of any independent set/group cansimultaneously share the spectrum. However, the undirectedgraph which was used in all these existing works fails tomodel the interference among base stations who bid with aset of different coverage sizes. In fact, the mutual interferencebetween any two bidders should be measured at multiplelevels rather than only as a binary “yes” or “no” (usingundirected graphs). To that end, we construct a mixed graph tofacilitate the interference negotiation among bidders. We thenprove that the winner determination problem in the formulatedmulti-attribute auction is in fact NP-hard. A heuristic winnerand coverage range determination algorithm is then designed.Note that the most relevant prior work to ours is the jointpower and channel allocation scheme [12]. However, similarto all existing works, the authors in [12] failed to capturethe interference among bidders with variable coverages butassumed a given conflict graph (for granted).

We incorporate the above into a spectrum sharing frame-work called Size-Negotiable Auction Mechanism (SNAM).Taking the LSA architecture [2] [13] shown in Fig. 1 as astudy case, spectrum allocation to all the base stations canbe managed by a centralized calculator and then the resultwill be announced to all the base stations through the LSAController. In terms of the auction efficiency, SNAM offersbidders a “second chance” to shrink their coverage areas to wina spectrum chunk. That helps to improve not only spectrum’sspatial efficiency but also the seller revenue and the buyersatisfaction. Our major contributions are as follows:• We propose a novel economic tool, namely SNAM

that exploits the unique feature of radio spectrum asa merchandise item: the bidder’s ability to adjust itsradio coverage. The tool allows the secondary biddersto simultaneously bid in an auction and negotiate theircoverages for the spectrum chunks. Our negotiable auc-tion mechanism is inspired by the empirical analysis andcomparison of auction and negotiation in economics [4].

• To facilitate the negotiation of bidders in SNAM, weconstruct a mixed graph to better quantify the interferencebetween spectrum licensees. To our best knowledge, thisis the first effort to model the interference problem ofspectrum auction using a mixed graph approach. Shrink-ing the coverage can improve the buyer satisfaction whilenot harming the seller revenue.

• SNAM is proved to be truthful and individually rational.Intensive simulations show that by better coordinatingcoverage regions of bidders, SNAM significantly im-proves the spectrum’s spatial efficiency. That leads to

dramatic improvement of the seller revenue and buyersatisfaction. The auction’s truthfulness is achieved at thecost of the revenue. However, we design a novel groupingprocess that guarantees the truthfulness with a lower costthan those in the literature, e.g., [6] [7] [14].

• The winner determination and payment rule in SNAMrelies on the bid per unit space and coverage area. Thisgives small bidders/firms who request small coverageareas a fair ground to compete with large bidders likeMobile Network Operators (MNOs).

In Section II, we present challenges in spectrum shar-ing market, the problem formulation, and bid processing.In Section III, we formally describe the details of SNAM.An example is illustrated in Section IV. The properties andcomplexity of SNAM are analysed in Section V. In SectionVI, simulation results are shown and discussed. Related worksare reviewed in Section VII. Conclusion and future work arefinally summarized in Section VIII.

II. PRELIMINARIES

A. Challenges

Incomplete information: The potential interested base s-tations could come from different MNOs. Due to security orprivacy considerations complete information in the market isnot possible. Hence they rely on LSA/SAS to coordinate theinterference.

Economic properties: In auction design, truthfulness isconsidered important because it can avoid bid manipulationwhere a bidder may cheat by declaring an untruthful bidinstead of a true valuation for the purpose of gaining a higherutility. Another economic property is individual rationality thatcan guarantee everyone in the auction cannot get a negativeutility, which is equal to its valuation minus payment.

Spatial efficiency. Besides the economic properties, thespectrum auction should also consider the spatial efficiency. Aconflict graph is widely used to allocate spectrum, but the con-struction of a graph and the graph processing have significantinfluences on the allocation performance. An undirected graphfails to capture the heterogeneity in coverage sizes of spectrumbidders. Furthermore, the base stations can shrink/negotiatetheir coverages and to win (“gaining a smaller pie is betterthan losing everything”), thus improving the spectral spatialefficiency.

B. Problem Model

We consider a single-round sealed auction in which N basestations play as bidders who bid for a set of 1, 2, ...,Midentical spectrum chunks from the auctioneer, i.e., spectrumsharing systems of LSA or SAS. Due to the privacy/securityissue each buyer has no knowledge of the others, the auction-eer has to coordinate the interference between them. For thatpurpose, every base station should also report its geolocation.Let (li, ri, bi) denote bidder i’s bid profile, where li is itslocation, ri is the set of requested coverage ranges and bi isthe bid for each unit space (e.g., $ per square meter).

Each base station registers K alternative coverage ranges,denoted as ri = (ri1, ri2, . . . , riK). In existing works [9-23],

3

K=1 and the interference status between any two biddersis modeled in a binary manner: “yes” (i.e., cannot simul-taneously share a band) or “no” (i.e., can simultaneouslyshare). To ease the exposition when K is large, we assumeeach bidder has two options for its requested coverages (i.e.,K=2). Specifically, a base station can customize an alterna-tive smaller interference-free range as a negotiable size ifthe original (large) coverage conflicts with others. Formally,ri = ri1, ri2, where ri1 ≥ ri2 and the ratio of these rangesis defined as

θi =ri2ri1∈ (0, 1]

which captures the flexibility of bidders in negotiating theircoverages. In two extreme conditions, when θi=1 (or K=1),no bidder wants to negotiate its coverage, and when θi is closeto zero the bidder shrinks the range very much.

We emphasize that SNAM is rooted from recently proposedspectrum sharing architectures by FCC and ETSI. The con-cept of coverage area in SNAM is inspired by the practicaldefinitions of protection and exclusion zone in LSA [2]and SAS [3]. Note that in a region, as the distribution ofusers/customers can follow any rule (e.g., uniform or normaldistribution), a buyer/bidder does not have to bid for a largearea when the buyers are concentrated in a small area. Therequested coverage range set depends on the buyer’s individualconditions and strategies.

Let (m, γi, pi) denote the determined result of bidder i,where pi is the payment of spectrum chunk m ∈ 1, 2, ...,M,within the interference-free range γi ∈ 0, ri1, ri2. Whenγi = 0, bidder i loses with payment pi = 0, and when γi = ri1bidder i can use the large coverage, while γi = ri2, bidderi has to shrink its coverage range with a lower satisfaction,which is defined as

ηi =

(γiri1

)2

∈ 0, θ2i , 1. (1)

After range determination the total bid of bidder i over therequired area is

Bi = biγ2i π. (2)

Assume that buyer i’s true valuation of a spectrum chunkper unit space is vi (e.g., $ per square meter) that dependson its business efficacy and criticality of having the spec-trum chunk (one may refer to [15] for the spectrum’s valuedetermination). Note that the true valuation vi of bidder i,while using a winning spectrum chunk, is assessed on thebidder’s effective area/coverage Ai. The effective coverage(a private information) defines the maximum coverage overwhich a bidder can capitalize from using the spectrum chunk.Beyond this effective area, the valuation vanishes (i.e., vi = 0)as additional coverage is neither profitable (e.g., desserts orjungles where no user/demand/traffic presents) nor possible(e.g., due to network planning or hardware/base-station ortransmit-power regulation limit).

Let Ui denote buyer i’s utility and it can be written as

Ui(ri, bi) = vi min(γ2i π,Ai)− pi (3)

which is the difference between the value capitalized by

using a spectrum chunk and the buyer’s payment. Here, weassume that with additional spectrum chunks, the base station’scapacity can be nearly linearly expanded (w.r.t to spectrumbandwidth). Additionally, the coverage area of a base stationis determined via its transmit power which can be flexiblytuned with various power control mechanisms.

Although the utility model in (3) is simple, it is sufficientfor us to capture two facts. First, the utility function is thedifference of the revenue and the cost of the spectrum overthe granted coverage. Second, the utility function is non-decreasing w.r.t. the granted coverage area. In our work, tofocus on the coverage negotiation (the major contribution ofSNAM), we adopt a simple model from prior works in [6][14]. In practice, SNAM can adopt any utility model that canbe written in the form of (3) with the above two properties.

Let M denote the allocation mechanism, and we have

(m, γi, pi) =M(bi, ri, li, b−i, r−i, l−i) (4)

where −i denotes all the bidders except bidder i.In this paper, the mechanism is evaluated from the following

criterion:• Individual rationality [6] [7] [14]: under the allocation

mechanism M the utility Ui(ri, bi) of a bidder i shouldbe non-negative, Ui(ri, bi) ≥ 0.

• Truthfulness [6] [7] [14]: a bidder cannot improve its util-ity by submitting a cheating bid, Ui(ri, vi) ≥ Ui(r′i, bi).

• Spatial efficiency: the total coverage area realized by eachspectrum chunk. We originally introduce to measure theperformance of a spectrum allocation algorithm in termsof the spatial coverage, formally defined as:

S =

∑Ni=1 γ

2i π

M. (5)

• Buyer satisfaction: it is defined as the ratio of the numberof winners to the total requesting buyers [6] [7]. It is usedto measure how much a spectrum allocation mechanismcan satisfy the buyers.

B =

∑Ni=1 ηiN

. (6)

• Seller revenue: it is the capital gain of the spectrumowner for trading his/her spectrum, a concept used inboth SAS and LSA [6] [7] [8] [14] [16] [17] .

R =

N∑i=1

pi. (7)

C. Bid Processing

The bid processing involves information exchanging anddecision making between the LSA Repository/Controller andthe sealed bids from different base stations, as shown in Fig. 2.As a direct access point, a base station plays an important rolein managing mobile devices and allocating resource to them.Therefore, we suggest that the available spectrum chunk isfirst allocated to a base station, then the base station furtherserves its customers.

SNAM can be fitted directly on the existing LTE systems,where a base station can register its bid request/profile via the

4

Incumbent(s) LSA Controller/Repository Base station(s) Mobile devices

Geolocation (space)

Time (duration)

Frequency

Allocate spectrum chunk(s)

Access to LSA spectrum chunk

Idle spectrum chunk(s)

[F1] Broadcast the available spectrum with details,

according to the information from repository

[F2] Each interested base station reports its bid profile

(l, r, b), namely location, range set and bid in unit space

[F3] Controller: Winner determination/payment,

authorize the winning base stations

[F4] Allocate resource blocks within LSA

spectrum chunk to terminal users

Withdraw spectrum chunk(s)

[F5] If mobile users move out of this area

[F6] Withdraw LSA resource blocks And let

mobile user switch back to primary band

[F7] Time is up for this LSA spectrum chunk /

Withdraw the spectrum from the base stations

[F9] Turn off command confirmation / Update new

available unit information

Withdraw LSA spectrum chunk

[F8] Vacate LSA band and switch to primary band

Fig. 2. Bid processing: Incumbents will update their available spectrum information to the repository and then the interested base stations will bid for thespectrum and submit their bid profiles. If a base station wins it can provide its users/customers with shared licensed access.

interface X1 through the Evolved Packet Core (EPC) and IPMultimedia Subsystem (IMS) [18] to the auctioneer controller.The very mild communication overheads could be put in amessage packet that contains one bid tuple as (l, r, b) fromeach bidder and one determination result tuple as (m, γ, p)from an auctioneer controller.

SNAM targets fine timescale auctioning. Specifically, thecustomer flow during a period of time in a weekend orweekday is predictable. If a base station wins the spectrum,then these venues can provide good services. We suggest thatSNAM runs hourly (but can be at a finer level as well).

Information broadcast: In the LSA framework we assumethat Incumbents will update the information about their avail-able spectrum chunks in the LSA Repository. This can bebroadcasted by the LSA Controller to all the base stations inthat region.

Bid submission: After receiving the available informationeach base station will then decide the bid profile, includingthe coverage range set and bid based on its terrestrial property,business plan, RF plan, and other technical aspects.

Winner determination and result announcement: asaforementioned, the undirected graph-based auction is inappli-cable in our case. To accommodate the coverage negotiation, inour work, we construct a mixed graph G = (V, E), representedby an adjacency matrix G, to let the auctioneer make theallocation decision aiming to improve the spatial efficiencyand at the same time guarantee that the auction is economic-robust. After the auction, winners and their granted coveragesare announced.

III. DETAILED SNAMA. Interference Levels

As aforementioned, unlike previous undirected graph basedschemes [6] [7] [8] [14], the mixed graph in SNAM canquantify interference into five levels instead of two (“yes” or“no”). We model the coverage area as a circle and use therelative positions of the two circles to measure the interferenceconditions. By comparing the relationship between the sum of

TABLE IFIVE LEVELS OF INTERFERENCE

Level Positions Graph Explanation

1 i j ji

Extremely High. Two BSs aretoo close to make anyconcession. Gij = 0, Gji = 0.

2 i jji

Simultaneous concessions.BS i and j have to makeconcessions at the sametime. Gij = −1, Gji = −1.

3 i j ji

Only one concession. BSi uses a small range whileBS j uses a large one.Gij = −1, Gji = 1.

4 i jji

Either concession. Need afurther determination.Gij = 1, Gji = −1;or Gij = −1, Gji = 1.

5 i jji

No concessions. BS i and j arefar away from each other. Theycan share the same spectrum.Gij = 1, Gji = 1.

the radii and the distance between the centres of the circles,we can quantify the interference as one of five distinct levels,as shown in Table I. For any two bidders i and j which aredij apart, their mutual interference is quantified from Level 1to Level 5 using the below inequalities (8)-(12):

Level 1: dij < ri2 + rj2 (8)

Level 2: ri2 + rj2 ≤ dij < min(ri1 + rj2, ri2 + rj1) (9)

Level 3: min(ri1 + rj2, ri2 + rj1) ≤dij < max(ri1 + rj2, ri2 + rj1)

(10)

Level 4: max(ri1 + rj2, ri2 + rj1) ≤ dij < ri1 + rj1 (11)

Level 5: dij ≥ ri1 + rj1 (12)

From Level 1 to Level 5, the mutual interference decreasesfrom extremely high to none. In Table I, for Level 1, a plain

5

line between the two nodes denotes that interference is sosevere that even at their lowest transmit powers, both of themcan not operate simultaneously. In Level 2, a double-headedarrow between the two nodes denotes that both of them have tomake a concession if they want to win. If one node is pointedby a single-headed arrow, it has to make a concession, but theother one does not need to, as shown in Level 3. Two single-headed arrows denote that either of the base stations has tomake a concession, as shown in Level 4. In this case, thewinner will be further determined by comparing their overallarea. In Level 5, if there is no edge between two nodes, itmeans that the two base stations can simultaneously share thesame spectrum chunk using their large ranges.

Note that the distance-based interference model is only usedfor the purpose of constructing the mixed interference graph.In practice, our coverage negotiation auction mechanism S-NAM can adopt any mixed interference graph as the input,regardless of which interference model is used. In other words,SNAM can accommodate any interference model that is usedto construct a mixed interference graph. For example, in thespectrum sharing frameworks SAS (proposed by FCC) andLSA (proposed by ETSI), the interference between Incumbentsand other tiers are captured through the concepts of protectionand exclusion zones [2] [3].

B. Constructing a Mixed GraphThe auctioneer generates a mixed graph G by using the

above definition of bidders’ mutual interference levels. Ev-ery interference level corresponds to either a directed or anundirected edge. Each element Gij in the adjacency matrix Gadopts a value in 0, 1,−1. Specifically, Gii =1 to capturethe fact that a node adjacent to itself and do not interfere toitself by using a large range. Moreover, every node has threepossible interference statuses to the others (j 6= i): Gij=1denotes that base station i can use a large range relative to thatof base station j; Gij=-1 denotes that base station i should usea small one relative to that of base station j; Gij=0 denotesthat base station i interferes to base station j seriously. TableI specifies how the auctioneer maps the five levels of mutualinterference to the adjacency matrix G.

Additionally, Level 4 still needs a further judgement, de-pending on their area summation. If

r2i1 + r2j2 ≥ r2i2 + r2j1, (13)

then bidder i will use the large area while bidder j uses thesmall area. Note that even when K is greater than 2, the keypoint is to maximize the overall coverages of any two buyers.The algorithm for mixed graph construction is described inAlgorithm 1 and its complexity is stated as follows.

Theorem 1: For N bidders of which each submits K cover-age ranges, the complexity of constructing their correspondingmixed interference graph is O((KN)2).

Proof : In Algorithm 1, it first needs to determine all possibleinterference levels between two bidders (the “switch” loop),resulting O(K2) complexity. There are two outer “for” loopsthat explore all bidders with complexity of O(N(N−1)/2) =O(N2). Hence, the combined complexity of the 3 loops toconstruct the mixed interference graph is O((KN)2).

Algorithm 1 Construct a mixed graphInput: Bid profiles of N biddersOutput: Interference Mixed Graph: the adjacency matrix G

1: for i=1:N do2: Gii ← 13: for j=(i+ 1):N do4: Check the interference Level between base stationi and j by (8) - (12).

5: Switch Level6: case 1: Gij ← 0, Gji ← 07: case 2: Gij ← −1, Gji ← −18: case 3: Gij ←1,Gji ←-1 or Gij ←-1,Gji ← 19: case 4: Gij ← ∓1, Gji ← ±1 determined by (13)

10: case 5: Gij ← 1, Gji ← 111: end for12: end for13: return G

C. Winner Determination

An ideal auction mechanism should simultaneously max-imize the revenue and maintain its economic robustness.Assuming that the bidders are truthful in revealing theirvaluations of the spectrum, the spectrum allocation problemis to assign the spectrum to independent nodes so that therevenue is maximized while no two bidders mutually interferewith each other. We first show that finding the independentnodes to form groups is NP-hard.

Theorem 2: The spectrum allocation problem that maxi-mizes the total revenue in (7) under interference constraints isNP-hard.

Proof : We assume that the above spectrum allocation prob-lem is not NP-hard. Hence, for the special case θ = 1 in whichthe mixed graph that we constructed becomes an undirectedgraph, there exists a polynomial time solution to maximumweighted independent set of the undirected graph [19]. Thatcontradicts to the fact that maximum weighted independent setis an NP-hard problem [20].

Not only does the NP-hardness of the spectrum allocationproblem make the winner determination challenging but alsothe strategic actions of the bidders who may not be truthfulin revealing their valuations. However, to achieve the revenuemaximization and truthfulness simultaneously is impossible,because to guarantee the truthfulness the pricing should beindependent of its own bid but based on the harm they causeto other bidders [21] [22]. For example, in the second priceauction, the highest bidder pays as much as the second highestbid, and the difference between the highest bid and secondhighest bid is the loss to guarantee the truthfulness. In thefollowing, we propose a winner determination mechanism thataims to find a better trade-off between revenue maximizationand auction truthfulness.

Unlike conventional merchandise, spectrum can be reusedsimultaneously by a group of bidders who do not interferewith each other. Such a group of bidders corresponds toa group of vertices of which any two nodes xi, xj ∈ Vhave no edge between them. Each group will be treated asa super bidder in the following spectrum allocation, then the

6

immediate questions are (i) how to group these nodes, (ii) howto determine the group bid, and (iii) how much to charge eachmember in a group. Notationally, the nodes are grouped asΩ1,Ω2, . . . ,ΩL, and let ΩBl denote the group bid of group l.

The following are three steps to iteratively form groups andthe algorithm is shown in Algorithm 2.

Algorithm 2 Winner determinationInput: Adjacency matrix G, number of available spectrum

chunks M and bids biOutput: GroupsΩl, paymentspi, determined rangesγi

1: l = 02: while 0 ∈ G or |G| > 1 do3: G′ ← G4: l← l + 15: while 0 ∈ G′ do6: delete the higher degree node from G′

7: end while8: for i = 1 : |G′| do9: if ∃j with G′ij = −1 then

10: γi ← ri211: else if only if ∀j,G′ij = 112: γi ← ri113: end if14: end for15: put the remaining nodes in group Ωl16: find out the minimum bid in group Ωl: Blα ←

min(Bl1, Bl2, . . . , B

ln) (using (2))

17: abandon the minimum bid in group: Ωl ← Ωl\α18: calculate the bid of group l: ΩBl = |Ωl|Blα19: remove Ωl from G20: end while21: L = l22: pick up the min(L,M) highest group-bid (ΩBl ) groups as

winning groups and allocate each group with one spectrumchunk m

23: the bidders in the same winning group Ωl will equallyshare the group bid ΩBl , as much as pi ← Blα

24: set the losers’ payment pi = 0, γi = 025: return Ωl, pi, γi, m

Step 1: Dropping seriously interfering bidders.First of all, to make sure all the bidders in a group can coexist,the node that Gij = 0 should be dropped iteratively. Thosebidders who seriously interfere (in Level 1) to the others aredropped from the mixed graph and the higher degree willbe dropped first. For example, if an edge eij = (xi, xj) is0, and bidder i’s degree deg(xi) is higher than bidder j’sdeg(xj), bidder i is dropped. This is because a bidder withhigher degree interferes to more neighbouring bidders. Thosedropped nodes will be put forward to the next iteration.

Step 2: Interference-free area judgement.After above processing, it is possible that bidder i can use alarge range to bidder j but has to use a small range to basestation k, namely Gij = 1, Gik = −1. Consider the overallfriendly sharing environment, one has to adopt the small rangeto all the neighbouring bidders. For example, in Fig. 3, Gij isforced to be −1. Therefore the determined range of bidder i

j i k j i k

Fig. 3. The bidder i’s range will be forced to shrink.

2 4 3 8 6

9 5 1

2 4 3 8 6

9 5 1

10 7

2 4 3 8 6

9 5 1

10 7

6

1

Group 1

Group 2

Group 2

Group 1

Group 3

Group 1

Group 2

Group 3

TRUST:

SMALL:

SNAM:

Revenue is low,

but spatial

efficiency is

high

Revenue is

high, but

spatial

efficiency is low

Both revenue

and spatial

efficiency are

high

10 7Group 3

Fig. 4. In TRUST, winners pay as the second highest group bid, the revenueloss is the difference between the 1st and 2nd highest group bid. In SMALL,winners equally share the group bid, but the minimum bid in the group willbe sacrificed and the nodes’ space is wasted. In SNAM, in every iteration theminimum bid is not sacrificed but moved into next iteration.

is γi = ri2, if ∃j, Gij = −1; and otherwise, γi = ri1, if andonly if ∀j, Gij = 1.

Step 3: Group bid calculation.Since the ranges of bidders are determined, then the to-tal bid of a bidder in group is easy to get. If there aren nodes in a group Ωl and let Bl1, Bl2, . . . , Bln denotetheir total bids, and the minimum total bid in the group isBlα = min(Bl1, B

l2, . . . , B

ln). All the nodes are independent

and can coexist, and the minimum bidder α will be treated asthe benchmark Blα but be abandoned. The remaining nodesautomatically form a group Ωl = Ωl\α, and the group bid is:

ΩBl = |Ωl|Blα (14)

where |Ωl| is the size (number of nodes) of the group. Allthe nodes that are abandoned (in Step 1 and 3) will be movedinto the next iteration of the group formation. The next groupwill be formed by repeating Step 1, 2, and 3. The groupingprocess continues until only one node left.

To facilitate the truthfulness of bidders in an auction, thewinning buyer’s payment should be made independently fromits bids [23]. Therefore, in the above, we abandon the mini-mum bidder (the dependent bidder), or the benchmark node.However, we observe that either abandoning the minimumbidders in all the groups e.g., [14] or abandoning the entiregroup with the lowest group bid e.g., [6] would cause a largeloss in both revenue and spectrum’s spatial efficiency. Hence,instead of removing them completely, in SNAM, we “recycle”the benchmark nodes by putting the loss into each iteration,and then put the minimum ones to the next iteration. Finally,only one bidder is sacrificed, as shown in Fig. 4.

Step 4: Final winner determination.After all the nodes are formed into groups Ω1,Ω2, . . . ,ΩL, themin(L,M) highest groups win and each member in the same

7

group will equally share their own group bids. Specifically,for buyer i in a winning group Ωl, its payment pi is given as:

pi = ΩBl /|Ωl| = Blα. (15)

Note that if M > L, then bidders who are in need ofadditional spectrum can join another auction for the rest ofM − L spectrum chunks. Additionally, although SNAM isa single-round auction with multiple (M ) identical spectrumchunks, it can also accommodate the case of heterogeneousspectrum chunks. In such a case, we can simply set the numberof available chunks M = 1 (i.e., trading with one chunk ata time). The following chunks are then traded in the nextauctions.

SNAM targets fine timescale auctioning. The auction canstart as early as there is a demand and an ideal spectrum chunkis registered for reuse. In Section V, we show that SNAM’scomplexity is polynomial w.r.t. the number of bidders and thenumber of requested range. Such a low complexity enables itto be implemented in a very fine timescale (e.g., hours or evenminutes).

From the winning determination, we can observe that S-NAM can provide small and large firms likely equal oppor-tunity to access the spectrum by considering their coveragerequests. In fact, SNAM aims to maximize the total revenuethrough improving the overall coverage, instead of directlymaximizing the revenue. Specifically, from the group bidcalculation, SNAM favors to accommodate a higher number ofbuyers other than a single or few buyers with large coverage.Additionally, the winner determination and payment rule inSNAM relies on the bid per unit space and coverage of theleast competitive bidder (the benchmark) other than the totalpayment. This gives small bidders/firms who request smallcoverage areas a quite fair ground to compete with larger ones.

IV. AN EXAMPLE

In this section we provide a simple example to demonstrateSNAM. Assume that one seller registers an available spectrumchunk in the geolocation database in a region, where there arefive buyers A,B,C,D,E with bids and negotiable rangeslisted in Fig. 5. In this example, we compare the significantdifferences between SNAM and the undirected graph basedapproaches TRUST [6] and SMALL [14].

In Fig. 6, we present how these five nodes are forms ingroups under TRUST and SMALL. The conflict graph in Fig.6(a) is modeled as all the base stations using large ranges.Under TRUST, the group bid is defined as the lowest bidmultiplied by the group size, |Ωl|min(Ωl). TRUST’s paymentrule is that the winning groups will pay as much as the highestlosing group. For instance, the winning group is B D, andthey altogether pay 228.91 as much as group E. Since thereare two winners out of five bidders, the buyer satisfactionunder TRUST is 40%. On the other hand, SMALL’s groupbid is defined as the lowest bid multiplied by the group sizeminus one, (|Ωl| − 1) min(Ωl), and the payment rule is thatwinners will equally share the group bid. The revenue, spatialefficiency and buyer satisfaction are given in Fig. 10.

SNAM lets each base station have a different negotiablerange ratio as shown in row “ratio” in Fig.5(b). Fig. 7 shows

A

B

C

D

E

(a) Five base stations’ requirements for licensed areas.

A B C D E

bid/unit 0.8 0.5 0.7 0.8 0.9

r1 12 10 7 8 9

r2 10.2 7 5.6 6.8 8.1

ratio 0.85 0.7 0.8 0.85 0.9

Bi, γ=r1 361.73 157 107.7 160.77 228.91

Bi, γ=r2 261.35 76.93 68.93 116.15 185.41

(b) Bid profiles of five base stations

Fig. 5. A simple example

EDC

B A

(a) Undirected graph.

Group Min bid Group bid Winner(s)

AC 107.7 215.40

BD 157 314 BD

E 228.91 228.91

TRUST

(b) Allocation result under TRUST

Group Min bid Group bid Winner(s)

AC 107.70 107.70

BD 157 157 D

E 228.91 0

SMALL

(c) Allocation result under SMALL

Fig. 6. Allocation results of the approaches based on undirected graph.

E

A

DC

B

(a)

E

A

DC

B

(b)

1

1

1

1

1

-1

1

-1

1

1

1

1

1

1

1

-1

1

1

-1

-1

1

1

1

A B C D E

A

B

C

D

E

G=

(c)

Fig. 7. Construction of a mixed graph. The pointed nodes need to shrinkwhile the pointing nodes can use large range. (a) the edge between any twonodes can be constructed as Table I; (b) For nodes C and D in Level 4, afurther decision is needed by (13); (c) adjacency matrix G.

the mixed graph and its adjacency matrix for the bidders. Theinitial mixed graph is shown in Fig. 7(a), then for node C andD, according to the further determination of the InterferenceLevel 4 in (13), the mixed graph turns into Fig. 7(b), becauseof r2C1 + r2D2 < r2C2 + r2D1 node C uses small range. Fig.8 provides the SNAM’s grouping process, Fig. 9 lists thecalculation of group bid, and Fig. 10 visually shows thecomparison of the allocation results. The pink circle is thebenchmark node, green circles are winners, and particularly,dark green circles are shrinking areas.

8

E

A

C

B

D

(a)

E

A

C

B

(b)

B

D

(c)

B

D

(d)

Fig. 8. Group formation: (a) Group 1: Dropping seriously interfering and highdegree bidder D; (b) Group 1: Benchmark node B is sacrificed; (c) Group2: The dropped node D and benchmark node B are moved into a seconditeration. (d) Group 2: The last benchmark node B is sacrificed.

Buyer

A 0.8 10.2 261.3

B 0.5 7.0 76.9

C 0.7 7.0 107.7

E 0.9 8.1 185.4

(a)

Buyer

B 0.5 10.0 157.0

D 0.8 8.0 160.8

(b)

Fig. 9. Group bid calculation: (a) Group 1: A,C,E form a group, and thegroup bid ΩB

1 = 76.9 ∗ 3 = 230.7; (b) Group 2: D itself form a group.The last node B sacrificed, and the group bid is ΩB

2 = 157 ∗ 1 = 157.Therefore, the winning group is group 1: A,C,E.

SNAM TRUST SMALL

Spatial Efficiency 0.27 0.21 0.08

Buyer Satisfaction 51% 40% 20%

Seller Revenue 230.79 228.91 157

(a)

(b)

Revenue: ; Buyer Satisfaction: %; Spatial Efficiency:

(c)

Fig. 10. Comparison of allocation results of SNAM and undirected graphbased approaches. (a) Performance comparison; (b) Allocation result underSNAM; (c) Allocation result under undirected graph based approach.

V. SNAM PROPERTIES

A. Individual Rationality

Theorem 3: SNAM is individually rational, i.e. Ui ≥ 0.Proof: We have two cases: (a) If bidder i is a winner, its

payment is pi and is equal to the benchmark payment Blα thatis the minimum bid in group Ωl, i.e., Bi > Blα. Recalling theutility function of bidder i, we have:

Ui = vi min(γ2i π,Ai)−Blα= viγ

2i π −Blα

= Bi −Blα > 0.

(16)

(b) If bidder i is a loser, it is obvious that Ui = 0.Therefore, SNAM is individually rational.

B. Truthfulness

In the bid profile (li, ri, bi), the bidder i may manipulateits bid per unit space bi, its location, or its requested rangeof coverages to maximize its utility (defined in (3)). In the

sequel, we prove that SNAM provides a truthful auctioningmechanism in which buyers have no incentive or are unableto cheat on the above information.

Theorem 4: SNAM is truthful for all the bidders.Proof: We first show that buyers should be truthful in its

coverage range. Note that each bidder has its own choice toset its requested ranges, depending on the area over which itcan capitalize from using the spectrum (defined above as theeffective coverage area) as well as its own justification of therisk being rejected due to a large coverage request. Hence, allrequested ranges that are within the effective coverage area areconsidered truthful and part of the bidder’s strategy. However,the buyers may still cheat on the requested coverage range intwo cases:

Case 1: A buyer requests a small coverage to win thespectrum then uses the spectrum over a larger coverage. Underboth LSA and SAS, regulations and spectrum enforcementmechanism are assumed to be in place to enforce bidders toabide with its requested coverages (e.g., using the environmentsensing capability ESC in SAS [24], [25]). Interested readersare also referred to [26] [27] for similar spectrum monitoringapproaches. Hence, a bidder cannot manipulate its geolocationor use the winning spectrum outside its granted range γi.

Case 2: A buyer i inflates its requested ranges r′i =r′i1, r′i2 beyond its effective coverage area, i.e., r′2i1π ≥r′

2i2π > Ai. If the buyer wins the auction either with r′i1 or

r′i2 coverage, from the utility function in (3), we have:

U ′i(r′i, bi) = viAi − pi.

However, by bidding truthfully (i.e., within the effectivecoverage area) with requested ranges ri = ri1, ri2 whereri1 = ri2 =

√Ai/π, the buyer can attain the same utility

as above Ui = U ′i with a higher likelihood. This is becausethe range/coverage inflation leads to higher risk of interferingwith others, hence increasing the risk of being removed in Step1. On the other hand, if the buyer loses the auction with therequested range r′i we have: U ′i = 0 or Ui ≥ U ′i (due to theindividual rationality property). Hence, regardless of losing orwinning the auction, inflating the coverage requests beyondthe effective coverage area results in inferior utility, comparedwith a truthful coverage bid.

Next, we prove that for all strategic bidders in SNAM, theirbest strategy is to reveal their true type of spectrum valuationvi. To that end, we first have the following lemmas.

Lemma 1: If a bidder wins a spectrum chunk, the bidder’sgranted range γi is independent of its own bid bi.

Proof : For any winner in a group, its granted coverage rangeis adjusted in Step 1 and Step 2 of the grouping process.In Step 1 and Step 2, when there is a conflict betweenrequested coverages, the bidders’ coverages are adjusted forthe coexistence with more neighbors. This criterion is onlyrelated to the bidders’ locations and their requested coveragebut not their bids.

Lemma 2: For any winner i, its utility is a step function ofits bid bi (or Bi) (as shown in Fig. 11).

Proof : For any winner i in the winning group Ωl, its utilityUi = vi min(γ2i π,Ai) − pi depends on its payment pi = Blαand granted range γi. If bidder i is retained and the benchmark

9

BiBαl

Ui

Fig. 11. The remaining bidder i’s utility is a step function of its bid bi.

payment is Blα. After a set of nodes are formed in a group,their ranges are determined and fixed. When bidder i increasesit bid bi, even though the bidder i’s total bid Bi increases, itspayment (set by the benchmark bidder) does not change. Onthe other hand, if bidder i decreases its bid which is lower thanthe benchmark, then it will be the benchmark and be droppedand put forward to the next iteration. The grouping processin Step 3 continues. At the last iteration, if the bidder wins,its payment is then again independent of its bid (set by thebenchmark bidder in this iteration/group), if not, its paymentis 0.

Now, let’s assume that if buyer i bids truthfully by bi = viits utility is Ui with granted coverage γi and payment pi. Ifit cheats by bidding b′i 6= vi, its utility is U ′i with grantedcoverage γ′i and payment p′i. We have four cases:

(a) |γi| = 0, |γ′i| = 0: In this case, bidder i loses regardlessof cheating or not, and Ui = U ′i = 0, and there is nomotivation for buyer i to cheat.

(b) |γi| = 0, |γ′i| > 0: We first have Ui = 0. According toSteps 1, 2 and 3 a bidder can only become a winner (froma loser) by increasing its bid, i.e. B′i > Bi and if and onlyif the bidder happens to be a benchmark (with truthful bid),i.e., Bi = Bα (see Lemma 2). By reporting a bid b′i, the newbenchmark will be the second lowest bid B−2 (in the casewith truthful bid) that is greater than Bi. The bidder i with itsbid b′i needs to pay p′i = B−2 > Bi. We have:

U ′i = vi min(γ′2iπ,Ai)−B−2. (17)

Recalling Lemma 1, to win with bid b′i, the grantedrange/coverage is determined independently of their bids, i.e.,the granted coverage γ′i would be the same as that if the bidderwins by bidding with bi. Hence, we have:

Bi = viγ′2iπ ≥ vi min(γ′

2iπ,Ai). (18)

From (17), (18), and B−2 > Bi, we have U ′i < 0 which issmaller than Ui = 0.

(c) |γi| > 0 and |γ′i| > 0: In this case, the cheating biddoes not change the granted coverage (see Lemma 1) and thebenchmark payment Bα stays the same, so does the paymentp′i = pi = Bα. Then we have U ′i = Ui.

(d) |γi| > 0 and |γ′i| = 0: It is obvious that in this caseUi > 0 and U ′i = 0, the bidder prefers to bid truthfully.

From the above analysis, Ui ≥ U ′i always stands, socheating can not make the bidder obtain more utility.

C. Group Formation

Theorem 5: Along with the group formation process, the(1) group size and (2) group bid becomes smaller statistically.

Proof : (1) With the group formation running, the numberof remaining nodes become less after each iteration, thereforethe group size is no larger than the previous group statistically.

(2) The bids are uniformly distributed, so the expectationsof bids are the same. In addition, the group bid is defined asgroup size multiplied by the minimum bid in equation (14).Therefore, if the expectations of minimum bids in every groupare the same, then the group bid is mainly contributed by thegroup size. So the group bid of smaller group is lower.

This is illustrated in Fig. 17 from Section VI.

D. Complexity Analysis

Theorem 6: For N bidders, and K levels of coverage, thecomplexity of SNAM is O((K2 +N2)N2).

Proof : SNAM consists of Algorithm 1 and Algorithm 2.According to Theorem 1, the complexity of constructing amixed interference graph is O((KN)2). Algorithm 2 firstaims at finding the auction winners with three loops (twowhiles and one for) whose combined complexity is boundedby O(N2(N2 +N2)). Therefore, the overall time complexityof SNAM is bounded with O((K2 +N2)N2).

Note that O((K2 + N2)N2) is a polynomial w.r.t. thenetwork size N and the number of requested ranges K.SNAM is hence scalable with N and K (even when theyget larger). Additionally, SNAM is a single-sided auction.The whole process includes the bid submitting and winnerdetermination with the complexity of O((K2 + N2)N2) andcould be completed or calculated out in time scale of secondor less. Hence, we even do not need to set a time constraintfor each auction.

VI. SIMULATION AND DISCUSSION

In this section, we will evaluate the performance of SNAMthrough simulation and compare it to the undirected graphapproaches [6] [14].

A. Setup

We consider a certain region where heterogeneous basestations scatter (under either a uniform or normal distri-bution) in the normalized region of 1x1. To accommodatethe bidders’ heterogeneity in their coverage requests, bidsand spectrum valuation, we set parameters in our simula-tions as follows. Buyer’s range is randomly distributed in[0.07,0.14]=[0.1/

√2, 0.1

√2]. Valuation of the spectrum is ran-

domly distributed in [b0,1], here, b0 is a variable and reflectsthe dynamic range of bid, and b0 is studied in subsection E. Tomitigate the impact of randomness, we run SNAM for 10000times in MATLAB to evaluate its performance.

B. Comparison to the Existing Works

At first, one visual allocation result is shown in Fig. 12, andthe number of base stations is N=50. The initial interference-free area requirements are shown in Fig. 12(a). The dark greencircle denotes the shrinking area; the pink circle denotes thedeleted benchmark node for truthfulness guarantee; and thelight green circles denote the nodes without any concession

10

in Fig. 12(c). It is obvious that the overall allocated areaunder SNAM is larger than that under the undirected graphauction. So SNAM can improve spatial efficiency becauseof the negotiation mechanism. Besides the spatial efficiency,shrinking coverages also allows more base stations to accessextra shared spectrum, which brings a higher revenue andbuyer satisfaction.

We first compare SNAM with the Pure Allocation (PA) algo-rithm. Due to its NP-hardness, we run PA on scenarios with adecent number of bidders 10,15, and 20 so that the exhaustivesearch method can be affordable. Note that although PA canprovide the highest revenue, it is extremely time-consumingand generally not affordable for a large number of bidders.As can be seen in Fig. 13, SNAM can achieve more than87% revenue of PA. Moreover, SNAM yields slightly higherbuyer satisfaction over PA. It worth noting that under SNAMthe spectrum’s spatial efficiency is dramatically improved,compared with PA. This is thanks to the negotiations ofbidders in adjusting their coverages, thus improving the spatialefficiency and accommodate more buyers. The heavier thenetwork congestion is, the more apparent this advantage ofthe ability to adjust the coverage becomes.

We also compare SNAM to the existing work TRUST [6]and SMALL [14]. We let all the bidders randomly set theirrange ratio between [θ0, 1], and for the SMALL and TRUSTthe ratio is always 1. When θ0 varies from 0.1 to 1, thecomparisons are shown in Fig. 14. Setting the shrinking ratiotoo small is neither practical nor beneficial. When the ratio isset greater than 0.8, SNAM performs better than SMALL andTRUST in terms of spatial efficiency, buyer satisfaction andseller revenue. This is because if the ratio is small, the totalbid of a bidder is also small and it always is treated as thebenchmark and be abandoned in the group formation iteration.

The loss of the revenue is related to the payment rule.Everyone’s payment depends on the benchmark of the group,therefore, the difference between their total bid Bi and bench-mark bid Blα is the revenue loss.

C. Impact of Network Density and Range Ratio

Next, we examine the performance of SNAM in differentkinds of networks in single-unit auction when the number ofbidders varies from 50 to 500 and ratio varies from 0.1 to 1,as shown in Fig. 15. Here we try to find out the best ratiowhile varying the bidder density. It is obvious that no matterhow many bidders participate the auction, setting the ratiobetween [0.85 0.95] is the dominant strategy for the bidders,which means that the bidders can achieve the highest buyersatisfaction and for sellers, they can get highest revenue.

D. Dynamic Range of Bid Distribution

Bid distribution is defined as in [6] [7] to capture theheterogeneity of the bids made by all buyers. Without losingthe generality, in the paper, we assume the bid distribution isuniform across all bidders. From the payment rule in equation(14), we can find that how much one winner pays depends onthe minimum bid in a group (benchmark). To examine howthe bid distribution effects the revenue, we set the number of

bidders N=100, and the bid distribution is over [b0, 1]. Whenb0 is small, the dynamic bid range is large. Because when thedynamic range of bid becomes smaller, the difference betweenthe minimum bid and the other bid in a group becomes smaller.As shown in Fig. 16, SNAM’s degradation over SMALL andTRUST becomes smaller when b0 is less than 0.4 in terms ofrevenue, but the revenue becomes higher and higher from 0.4to 1. However, the spatial efficiency and buyer satisfaction arealways much better than SMALL and TRUST.

E. The Group Formation

The feature that allows the bidder with an alternative rangemakes the groups formed under SNAM accommodate morebidders. The benchmark node of group will directly affect theperformance. Since the bid, location and range are distributedin the same domain for all the bidders, the expectations oftheir total bids are also the same as

E[b1γ21π] = E[b2γ

22π] =, . . . ,= E[bNγ

2Nπ]. (19)

E[B1] = E[B2] =, . . . ,= E[Bn]. (20)

However, during the group formation process, we also findthe size of first formed group is no smaller than the later ones,recalling Theorem 5, which can be expressed as

Pr(|Ωl| > |Ωl+1|) > Pr(|Ωl| < |Ωl+1|). (21)

Expectations of benchmarks are the same because of (20),therefore the expectation of group bid should be

E[B1α] ≥ E[B2

α] ≥, . . . ,≥ E[Blα]. (22)

As shown in Fig. 17, the first few group groups formedunder SNAM have a higher number of members and largertotal area. The number of groups under SNAM is less orthe grouping process ends up quickly. Therefore, the groupformation speed of SNAM is faster than TRUST and SMALLwho use the same grouping scheme.

As a result, in a congested spectrum market, when thenumber of available spectrum chunks M is small (M N ),the spatial efficiency, seller revenue and buyer satisfactionunder SNAM are better than TRUST or SMALL. Along withthe increment of M , the difference between them becomessmaller, and finally the revenue turns equal, as shown in Fig.19 (c).

Fig. 18 compares the seller revenue and buyer satisfactionunder different bidder distributions. As can be seen, underthe uniform distribution, the seller revenue and the buyersatisfaction are higher than those under the normal distribution.This is because under the normal bidder distribution, thenodes/bidders are crowded around the center, making theinterference more severe. That leads to the lower revenue andthe lower buyer satisfaction.

VII. RELATED WORKS

The traditional manual auction for spectrum allocation isno longer suitable and efficient for dynamic spectrum accesssystems, such as LSA and SAS. Spectrum sharing betweendifferent MNOs should not only consider the interference

11

(a)

Seller Revenue:

0.21531

Buyer Satisfaction:28%

Spatial Efficiency:0.41445

(b)

Seller Revenue:

0.27133

Buyer Satisfaction:29.2547%

Spatial Efficiency:0.50207

(c)

Fig. 12. A visual allocation result comparison. (a) Base stations are uniformly distributed in a region and each has two options of interference-free range; (b)allocation result based on SMALL [14] the large range is considered as the interference-free range and the pink circle is the sacrificed node; (c) allocationresult based on SNAM: the light green nodes are the winners that can use large ranges, and the dark green nodes are the winners that can use small ranges.

10 15 20Number of bidders

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Spatial E

ffic

iency

10 15 20Number of bidders

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Buyer

Satisfa

ction

10 15 20Number of bidders

0

0.05

0.1

0.15

0.2

Selle

r R

evenue

SNAM PA

Fig. 13. Comparison of SNAM’s performance with PA.

0.2 0.4 0.6 0.8 1

0

0.2

0.3

0.4

0.5

0.6

0.7

Spatial E

ffic

iency

0.2 0.4 0.6 0.8 1

0

0

0.05

0.1

0.15

0.2

0.25

Buyer

Satisfa

ction

SNAM TRUST SMALL

0.2 0.4 0.6 0.8 1

0

0.1

0.2

0.3

0.4

0.5

Selle

r R

evenue

Fig. 14. When the ratio is set from [θ0,1], SNAM performs best over θ0 ∈[0.8,1]. Because too much shrinking the coverage makes bidder’s total bid lowand leads to losing in a group. If shrinking ratio is set greater than 0.8, the buyer satisfaction can be improved and so are spatial efficiency and revenue.

between them but also their selfish behaviors when sharing.Authors in [28] investigated the performance loss due toselfish behavior under a self-enforcing protocol. [29] [30]proposed contract-based approaches to solve the conflictingof sharing. To accommodate the above heterogeneity, on-lineauctions based on short intervals in the time domain and smallareas in the space domain [15] have recently been proposed.Zou et al. [31] considers an auction-based power-allocationscheme to solve power competition of multiple secondaryusers but cannot guarantee truthful behaviors. Sodagari et al.[10] presented a truthful spectrum auction mechanism but does

not consider spatial re-usability of the spectrum. In [6] [14] theproposed double auction mechanisms achieve not only spatialre-usability in geolocation by grouping bidders but also havean anti-cheating property through a proper choice of winnerdetermination and payment rule. However, the coverage ofthe base station is not taken into account. Researchers in[7] [8] [17] proposed mechanisms of truthful double auctionfor heterogeneous spectrum which considers heterogeneityfactors in frequency but not in ranges/coverages. Yang andLin et al. [32] [33] very recently proposed a group buying-based spectrum auction to provide small firms with more

12

(a) (b) (c)

Fig. 15. Impact of network density and ratio. (a) When the number of bidders in a certain region varies from 50 to 500, the spatial efficiency can reachthe maximal when the ratio is around [0.85, 0.95]; (b) When there are more bidders in an auction, the average buyer satisfaction is low, however, the buyersatisfaction is better when the ratio is around [0.85, 0.95]; (c) Accordingly, the revenue is better if ratio is set in [0.85, 0.95].

0 0.2 0.4 0.6 0.8 1

b0

0.42

0.44

0.46

0.48

0.5

0.52

0.54

0.56

0.58

Sp

atia

l Eff

icie

ncy

0 0.2 0.4 0.6 0.8 1

b0

0.4

0.45

0.5

0.55

0.6

0.65

0.7

Bu

yer

Sa

tisfa

ctio

n

SNAM TRUST SMALL

0 0.2 0.4 0.6 0.8 1

b0

0.05

0.1

0.15

0.2

0.25

0.3

Se

ller

Re

ven

ue

Fig. 16. The impact of bid distribution. If the dynamic range of bid distribution is large, then the minimum bid will hold back the group bid, so the revenueloss to guarantee the truthfulness is more.

0 2 4 6 8

Group Index

0

5

10

15

20

Gro

up

Siz

e

Bidder distribution:uniform

TRUST

SMALL

SNAM

0 2 4 6 8

Group Index

0

0.2

0.4

0.6

Sp

aria

l E

ffic

ien

cy

Bidder distribution:uniform

TRUST

SMALL

SNAM

0 5 10 15

Group Index

2

4

6

8

10

Gro

up

Siz

e

Bidder distribution:normal

TRUST

SMALL

SNAM

0 5 10 15

Group Index

0.05

0.1

0.15

0.2

0.25

0.3

Sp

aria

l E

ffic

ien

cy

Bidder distribution:uniform

TRUST

SMALL

SNAM

Fig. 17. The first few groups formed under SNAM are bigger than thoseunder TRUST/SMALL in both uniform and normal distributions.

opportunities in case that they cannot afford an entire spectrumchunk in a large region. Another significant issue is the privacy,for example, Li et al. in [5] presented PPER to protect users’bid privacy but the bidders are terminal user pairs rather thanbase stations. DEAR in [9] achieves approximate truthfulness,privacy preservation. However, the bidders are assumed to be

Bidder distribution

uniform normal

Se

ller

Re

ve

nu

e

0

0.05

0.1

0.15

0.2

Bidder distribution

uniform normal

Bu

ye

r S

atisfa

ctio

n

0

0.05

0.1

0.15

0.2

0.25

0.3

TRUST SMALL SNAM

Fig. 18. Performance comparisons of the seller revenue and the buyersatisfaction under different bidder distributions.

distributed in homogeneous conventional hexagons, while infuture spectrum market, base stations from different MNOsare heterogeneous and arbitrarily distributed.

VIII. CONCLUSION

We presented a hybrid approach of auction and negotiationfor spectrum sharing, namely SNAM. Unlike all existingauction-based spectrum sharing models in the literature thatstifles the communications between the seller and buyers,SNAM provides a channel for the seller and its buyers to

13

1 2 3 4 5 6 7

Number of Channels

0.45

0.5

0.55

0.6

0.65

Sp

atia

l E

ffic

ien

cy

1 2 3 4 5 6 7

Number of Channels

0

0.1

0.2

0.3

0.4

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ye

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atisfa

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Fig. 19. Impact of number of available spectrum chunks. SNAM has a more obvious advantage when the number of available spectrum chunks is less.

further negotiate their coverages. Considering the spatial effi-ciency in a licensed shared spectrum scenario, the mixed graphlets base stations from different operators make concessionswhen interference happens. Merging the area shrinking intothe grouping process can reduce the number of iterations andalso improve the spatial efficiency and buyer satisfaction, thuscontributing to a higher revenue. That is a main differenceto the existing works that form bidder groups based on onlythe undirected interference graph. As a result, our approachcan accommodate more base stations thus providing a faircompetition environment for small firms competing with largefirms for spectrum. Based on the analysis of the simulationresults, the importance of the large to small radius ratio for d-ifferent sizes of the interference-free area can be observed. Wealso prove that the proposed auction mechanism preserves theeconomic properties of individual rationality and truthfulness.Overall in the heterogeneous multiple NMOs’ networks, theproposed mechanism performs better than the undirected graphbased auction in terms of spatial efficiency, seller revenue andbuyer satisfaction.

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Huiyang Wang received the M.E. degree in Infor-mation and Communications Engineering from theBeijing University of Posts and Telecommunication-s, Beijing, China in 2014. She is currently workingas a PhD candidate in the School of Electrical andData Engineering at the University of TechnologySydney, Australia. During 2014 to 2017, she is pro-vided with the International Postgraduate ResearchScholarships (IPRS) by the Australian GovernmentDepartment of Industry. Her research interests in-clude resource allocation, game theory, graph theory,

applications in Internet of Things, and data engineering.

Diep N. Nguyen received his M.E. and PhD degreesin electrical and computer engineering from theUniversity of California, San Diego, CA and TheUniversity of Arizona, Tucson, AZ, USA, respec-tively. He was a DECRA Research Fellow withMacquarie University, a member of Technical Staffwith Broadcom, San Diego, CA, USA, and ARCONCorporation, Boston, MA, USA, and a Consultantfor the Federal Administration of Aviation on turningdetection of UAVs and aircraft, for the US AirForce Research Laboratory on Anti-Jamming. He is

currently a faculty member at the Faculty of Engineering and InformationTechnology, University of Technology Sydney, Australia.

Eryk Dutkiewicz received his B.E. degree in Elec-trical and Electronic Engineering from the Universi-ty of Adelaide in 1988, his M.Sc. degree in AppliedMathematics from the University of Adelaide in1992 and his PhD in Telecommunications from theUniversity of Wollongong in 1996. His industryexperience includes management of the WirelessResearch Laboratory at Motorola in early 2000s. Heis currently the Head of School of Electrical andData Engineering at the University of TechnologySydney, Australia. He has held visiting professorial

appointments at several institutions including the Chinese Academy of Sci-ences, Shanghai JiaoTong University and Macquarie University. His currentresearch interests cover 5G networks and medical body area networks.

Gengfa Fang received his Master in Telecommuni-cations from Zhejiang University and PhD in Wire-less Communications from the Institute of Com-puting Technology, Chinese Academy of Sciencesin 2002 and 2007 accordingly. From Oct. 2007 toMay 2009, he was a Researcher at the CanberraResearch Lab of National ICT Australia (NICTA) onWCDMA Femtocell project. From Jun. 2010 to Dec2010, he was working on Rural Broadband Accessproject at CSIRO as a Research Scientist. From 2009to 2015, he was with the Department of Engineering

Macquarie University. In 2016 he moved to UTS where he is now a SeniorLecturer.

Markus Mueck received the Engineering degreesfrom the University of Stuttgart, Stuttgart, Germany,and the Ecole Nationale Suprieure des Tlcommu-nications (ENST), Paris, France, and the Doctoratedegree in communications from ENST. He overseesIntels technology development, standardization, andpartnerships in the field of spectrum sharing. In thiscapacity, he has contributed to standardization andregulatory efforts on various topics such as spectrumsharing within numerous industry standards bodies,including the European Telecommunications Stan-

dards Institute (ETSI), Third-Generation Partnership Project, the IEEE, theWireless Innovation Forum, and the European Conference of Postal andTelecommunications Administrations (CEPT). He is an Adjunct Professor ofengineering with University of Technology, Sydney, Australia, and acts asan ETSI Board Member supported by Intel and as the general Chairmanof the ETSI RRS Technical Body (Software Radio and Cognitive RadioStandardization).